WASHINGTON — The Trump administration plans to aggressively push for tougher screening of asylum seekers that will make it vastly more difficult for migrants fleeing persecution in their home countries to win protection in the United States, a senior administration official told reporters on Tuesday.

The official said that President Trump ordered a shake-up of his top immigration officials in recent days because they were moving too slowly, or even actively obstructing, the president’s desire to confront the surge of migrants at the southwestern border. The asylum changes are among many policies the president wants to put into effect with a new team in place, the official said.

Mr. Trump denied on Tuesday that one of those changes would be to restart his policy of separating migrant families at the border, though he said that the act of taking children from their parents — which drew global condemnation before he abandoned it last summer — was effective.

“Now I’ll tell you something, once you don’t have it, that’s why you see many more people coming,” Mr. Trump said. “They are coming like it’s a picnic, because, ‘Let’s go to Disneyland.’”

The administration official, who spoke on the condition of anonymity even as Mr. Trump was making his remarks, said a modified version of family separation, in which parents are given a choice of whether to be separated or to accept indefinite detention alongside their children, continues to be under consideration.

But the so-called binary choice proposal is “not ripe for White House consideration” right now, he insisted, because the government does not currently have the detention space to hold families if the policy were put in place.

The asylum changes being envisioned could drastically alter the role that the United States plays as a refuge for people fleeing poverty, violence and war. American and international laws require it to allow migrants to request asylum once they come to the country.

But the official said that an initial assessment of the basis for a request for asylum — known as a “credible fear” screening — too often accepts the claim that the migrant was persecuted. The official also said that many more asylum seekers should be rejected during that first step.

Out of 97,728 completed interviews with migrants in the fiscal year that ended on Sept. 30, 2018, the United States Citizenship and Immigration Services confirmed a credible fear of persecution 74,677 times, according to an agency official.

Changes in the screening process could drastically lower those findings by requiring more proof from asylum seekers that they would be persecuted in their home countries. Screeners could also try to verify migrant claims by using State Department assessments of the threats that exist in those countries.

Immigrant rights advocates have feared for months that the administration would try to change the standards by which asylum seekers are judged in an effort to prevent more of them from coming into the United States.

The administration official blamed the delay in that effort on “deep state” bureaucrats at the Department of Homeland Security and even the president’s own political appointees in the department, whom the official described as lacking the management skills to push Mr. Trump’s agenda.

The official declined to name specific administration officials who have failed. But he made thinly veiled references to two top officials at the Department of Homeland Security: John Mitnick, the department’s general counsel, and L. Francis Cissna, the head of United States Citizenship and Immigration Services.

He said there was “clearly a track record” in which the president’s policies have not been advanced.

In his remarks on Tuesday, Mr. Trump falsely said that President Barack Obama had embraced the same policy of routinely separating migrant children from their parents at the border.

“President Obama had child separation,” Mr. Trump said during brief remarks in the Oval Office, where he was meeting with President Abdel Fattah el-Sisi of Egypt. “I’m the one that stopped it.”

Under Mr. Obama and President George W. Bush, immigration officials sometimes separated families when they had reason to question parentage or when there was evidence of child abuse. The Trump administration instituted a policy in which all families who crossed the border illegally were separated in order to allow the parents to be prosecuted under the administration’s “zero tolerance” policy. More than 2,700 children were separated from their parents at the border before Mr. Trump ended the policy in June 2018.

The president’s comments come after he shook up the senior ranks of the Department of Homeland Security, forcing the resignation of the secretary, Kirstjen Nielsen, and top immigration officials in a move that signaled a pending shift in immigration policies.

Also on Tuesday, the acting deputy secretary of homeland security, Claire Grady, who was next in line by law to become the acting secretary, submitted her resignation, according to a Twitter post by Ms. Nielsen. Ms. Grady’s resignation paves the way for Kevin McAleenan, the commissioner of Customs and Border Protection, to take the role.

Customs and Border Protection officials this week underscored Mr. Trump’s concern about illegal immigration by announcing that more than 103,000 migrants crossed the southwestern border in March without authorization, an increase from the more than 76,000 migrants who crossed in February.

“Just last month, we saw record numbers of family units and unaccompanied juvenile apprehensions in February, and unfortunately, March apprehension numbers are again record-setting and cause dire concerns for us,” said Brian Hastings, the chief of law enforcement operations for the Border Patrol.

Most of the migrants — 92,000 of the 103,000 — were apprehended by Border Patrol agents, meaning they crossed in between the ports of entry.

More than 53,000 of those migrants were members of a family, Mr. Hastings said, and most of those families were from Honduras, Guatemala or El Salvador.

In the first half of fiscal year 2019, Border Patrol agents apprehended more than 385,000 migrants on the border, more than double those apprehended during the same time last year.

Mr. Hastings said the Border Patrol can generally maintain 4,500 people in its custody. But it recently counted 13,000 migrants in its facilities, and he said the overflow has led to the release of families into cities along the border.

On Tuesday, White House officials announced that the president would appeal a judge’s ruling that blocked the administration’s “Migrant Protection Protocols,” which require some asylum seekers to remain in Mexico while they wait for their court cases.

Mr. Trump has recently commended Mexico for doing more to stem migration to the border, but the officials said they have not seen any effect on the number of people crossing it. “The numbers aren’t declining; in fact, we’re still seeing 3,000 apprehensions per day,” Mr. Hastings said.

Officials also revealed that among the tens of thousands of family members approaching the border each month, just 3,100 people who said they were traveling with relatives were found to have a fraudulent claim. Those people either said they had a child when the individual was over 18 or the group’s members were not really related.

Eileen Sullivan contributed reporting.

A version of this article appears in print on , on Page A12 of the New York edition with the headline: Trump Administration to Push for Tougher Rules on Asylum. Order Reprints | Today’s Paper | Subscribe